|Assuming that router is wireless capable, and has a properly configured and working wireless network (WLAN) you would connect the Kindle like you would any other device.|
Read the Kindle manual, pay special attention to the section on connecting to a WLAN. Follow the insttructions there.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.